This investigation presents a simple, widely tunable, and ultrasensitive sensor that is based on a leaky-guided multimode fiber interferometer (MMFI) operated under refractive-index-matched coupling. By use of a material with an appropriate dispersion profile around the MMFI as a cladding yields strong index-matched coupling, which performs ultrasensitive sensing in variations of the surroundings. Index matching at a single wavelength yields a coupling wavelength dip with a narrow bandwidth and a high extinction ratio of over 25 dB. The wavelength dip can also be effectively tuned, greatly shifting with a variation in temperature (T) or refractive index (RI), when the index-matched condition is satisfied. This work demonstrates that the proposed sensor responds sensitively to T with an extremely high tuning efficiency of 50 nm/°C and an excellent sensitivity to RI of 113,500 nm per RI unit.